please prove the identity and show your work
thanks
2007-02-05 19:43:28 · 4 answers · asked by blcklabelx 1 in Science & Mathematics ➔ Mathematics
LHS = (1/cos x) (1/sin x) - 2 sin x / cos x
= 1/(sin x cos x) . (1 - 2 sin^2 x)
= 2 / (2 sin x cos x) . (1 - 2 sin^2 x)
= 2 / sin 2x . cos 2x
= 2 (cos 2x / sin 2x)
= 2 cot 2x.
2007-02-05 19:48:46 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
By definition,
sec x cosec x - 2tan x = 2/sin 2x - 4sin^2 x / sin 2x
= 2(1- 2sin^2 x) / sin 2x
= 2 cos 2x / sin 2x
= 2cot 2x
as required.
2007-02-06 04:47:33 · answer #2 · answered by yasiru89 6 · 0⤊ 0⤋
LHS=1/(cosx*sinx)-2sinx/cosx=
=(1-2(sinx^2))/(cosx*sinx)
=(cos^2+sin^2-2*sin^2)/(cosx*sinx)
=cos2x/(sin2x/2)
=2cot2x
2007-02-06 03:57:45 · answer #3 · answered by QuizBox 2 · 0⤊ 0⤋
secxcscx-2tanx=
=1/sinxcosx-2sinx/cosx=
=(1-2sin^x)/sinxcosx=
=cos2x/0.5sin2x=
=2cot2x
2007-02-06 04:07:48 · answer #4 · answered by happyrabbit 2 · 0⤊ 0⤋